2 x Strong-Backed Labour costs 13.50 Echoes each (available in Wilmot's End, via "The Missing Woman" repeating storyline; Unlocked with Shadowy 110, a fine piece in the Game 1, and when Enjoying Lethal Prominence, via "A Rival in Power"). This step requires "a Zailor in the making 1" OR Connected: The Docks 20 (a worse option, because you have to cash in much of that connection).

If you intend to grind the resources to buy these components directly from the Bazaar Side-Streets, End Game Grinding has the best locations for doing so.

Buying A Specific Ship

As of July 2015, this section is still likely accurate.

So what else is needed?

All ships, save the Tramp Steamer, are exorbitantly expensive without fate. Costs below:

Zubmarine

Step 1:1 x A Copy of your Tale of the Future (can be written in the Empress' Court —this will not consume this item! you just need to have it to pass this step.)or
Have "a Scholar of the Correspondence" 3 (earned in the Forgotten Quarter via Archaeological Expeditions and reaching the Tomb of the Seven, then raised in the Forgotten Quarter as well — similarly, you just need to have this status to pass this step.)or10 x Fate

Gaining Zub Materials

The Lenses and Contraptions make the Zubmarine the hardest ship to acquire. Contraptions are straightforward to get in Wilmot's End, but take a very long time to get all 20 (21 total, given that all ships need 1 up-front).

Bejewelled Lenses are available only by buying them in the Bazaar Side-Streets. The seven total Magnificent Diamonds are the major problem here. You can try for the rare success from buying "A bag of low-quality diamonds" in the Side-Streets, but a more reliable way to gain them is as follows:

Grind Casing in the Flit using either the Gang of Hoodlums option, or — if lower-level — the failure-proof POSI Casing option.

Sell Casing to Criminals, also in the Flit. This also will significantly boost your Shadowy score — possibly the best way to grind Shadowy in the game.

Once you have Connected: Criminals 30 (at least), wait to draw the Implausible Penance card.

Choose Pugilism and Politics, then beat up the Minister. This will gain you 2 x Magnificent Diamond as well as 2 x Ostentatious Diamond. (Do not beat up the Underworld Kingpin — this will exchange 500CP Criminals for 500CP Society and increase Turncoat, and grant you no diamonds!)

Repeat this process until you have all 7 Magnificent Diamonds. (Consider gathering Connected: Criminals first, so you can grind other things while you wait for the Implausible Penance card to show up again.)

Update 1/30/16 — as of a few months ago, this option has changed. It now requires gathering Favours: Criminals. Notably, selling Casing to Criminals now does nothing but boost Shadowy.

Updated method follows:

Gather 7 Favours: Criminals. Note that this is the maximum number of Favours you can gain, and plan accordingly. You mostly need to gain Criminals Favours from cards, but fortunately, there are many cards which hand them out. Buy the Alluring Accomplice and the Ruthless Henchman from Redemptions at the Bazaar and wait for their cards, show people who's boss on the Gang of Hoodlums card (the Gang is acquired in the Bazaar side-streets and the best way to gain Casing) and lie to help a pickpocket on the Criminals card. There's currently no way to grind Favours outside of cards, but you can gain a few in the Carnival if you have no Renown: Criminals. (On the other hand, at Renown: 20, you unlock another card which also grants a Favour.)

Wait for the Implausible Penance card. If you draw it before you gain 7 Favours, so much the better; keep it in your hand until you gain all 7 Favours.

Choose Pugilism and Politics, then beat up the Minister. This will gain you 1 or 2 x Magnificent Diamond (50/50 chance) as well as 3 x Ostentatious Diamond. (Do not beat up the Underworld Kingpin, as this grants you no diamonds.)

This is all best done at the same time as grinding Whirring Contraptions in Wilmot's End, since it involves a lot of waiting for cards.

Majestic Pleasure Yacht:

Step 1:
10 x Touching Love Storyor
Or 3 Connected: Masters of the Bazaar (does not cost any of this quality, you just need to have it; in fact, you'll get a small reward for using this option: 2 x Dark-dewed Cherries)or10 x Fate and 1 x Whispered Secret

Step 2:5 x Comprehensive Bribe, 5 x Favours in High Places, 5 x Cellar of Wine, 5000 x Deep AmberA matter of luck: the odds are strongly against you here. Also, a Persuasive and Watchful check. Losing this contest will cost you one-fifth of your stake. Winning will cost you all of it and grant you the Yacht.
Note: It is possible to win this exchange very quickly… and also possible to lose it repeatedly for a very long time.or20 x Fate and 1000 x Deep Amber. Using Fate will cause you to succeed automatically, with no luck check (and comes with almost no extra cost, unlike the Zubmarine's Fate option).

Gaining Yacht Materials

Comprehensive Bribes are, unfortunately, best purchased in the Bazaar Side-Streets for the steep price of 300 x Romantic Notion, 30 x Vision of the Surface, and 6 x Touching Love Story. For all these items, this pretty much means grinding and up-converting Prisoner's Honey from your inventory. This is best done in Unfinished Business in Veilgarden; but if you want to gain Making Waves and have access to Court, the final option under Life of the Mind is almost as good. (Use Veilgarden if you'll also be grinding Stolen Kisses for Favours; you'll get a few Stolen Kisses via rare successes.)

To get 5 Comprehensive Bribes (you will need more unless you're incredibly lucky), this means 1,500 Romantic Notions, 150 Vision of the Surface, and 30 Touching Love Story. This means 16,500 Prisoner's Honey, or 330 actions if you use Veilgarden. (3,300 Prisoner's Honey / 66 actions for each new Bribe.)

If you up-convert Romantic Notions to Visions of the Surface the slow way, you can sometimes get a bonus Comprehensive Bribe on a rare success.

If you're okay with a luck grind, the Fidgeting Writer can provide the Bribes plus other goodies, but it's really chancy (and you'll have to grind materials for that instead).

Favours in High Places have multiple good sources. The two best ones are as follows:

The Affair of the Box grind, accessed by following the Mahogany Hall part of the story to completion (the short version is "raise Tales of Mahogany Hall through Variety is the Spice of Life, and it will unlock storylets as it gets higher; the grind itself appears in Spite once unlocked) rewards Stolen Kisses, which can be up-converted to Favours in High Places. You'll get all 5 through one up-conversion of 25 Stolen Kisses, which is nice.

You can cross-convert other items to the Influence category. Notably, you can grind Tales of Terror in the Flit, convert to Compromising Documents, and up-convert until you get your Favours. This will also give you a bunch of Making Waves.

Cellars of Wine also have multiple sources.

As with Favours, you can use the Affair of the Box grind, using it to get Strangling Willow Absinthe and up-converting. Also as with Favours, you'll get all 5 at once from 25 Broken Giant.

You can use the Velocipede Squad loop to get Broken Giant; slightly less efficient, but superior if you want to grind high-level Dangerous instead of Shadowy; at the end of the loop, use the Riot option and read the Riot Act.

You can also cross-convert items to the Wines category and up-convert them.

5000 Deep Amber is the easiest to get; the best grind is in Mahogany Hall by raising fires working for Jasper and Frank (needs Tales of Mahogany Hall 10, which you'll want to raise anyway to unlock the Affair of the Box grind, probably).

Which Ship Is Best?

As of July 2015, this section is partially accurate. Notes have been made throughout where changes are known.

The Majestic Pleasure Yacht is far and away the best ship, because it grants +2 BDR (in the form of +2 Respectable).

The Zubmarine is the second best ship, because it grants +1 BDR (in the form of +1 Bizarre).

The Swift Zee-Clipper is the third best ship, because of its unique card when zailing, but has much less value due to no BDR.

The Tramp Steamer almost as good as the Zee-Clipper due to card mechanics (take note that despite the flavor text, the Steamer is 100% reliable).

For more help determining which ship is best for you personally, read summary at the end of this overall section.

BDR

Because of how BDR (Bizarre, Dreaded, and Respectable) works and its importance to the end game gaining of Notability, the Yacht is the best ship (and the Zubmarine the second best). The other two ships provide no BDR and are therefore significantly less valuable.

The reason is that it's not about zailing. BDR boosts benefit you in your time in London — which will be 90% of your career, if not more. The other two ships provide no benefit outside of the zee. The ships were balanced for an earlier version of the game, when things were arranged differently.

A small extra benefit to the Zubmarine is that Bizarre is harder to gain than Respectable. Challenges that make use of Bizarre are rare, but exist. This is less of a benefit in the current (mid-2015) state of the game; the Yacht is still better because +2 total BDR from any source is superior to +1 BDR.

The difference is still fairly marginal, at 1 or 2 points. If you don't mind extra Making Waves grinding to reach the next Notability tier (each point of BDR is one less Making Waves level required), or don't care about Notability, or if you value something else more, or if you just like one ship better than another for aesthetic or roleplaying reasons, then just get the ship you like best.

Price

In terms of cost, unless you are extremely unlucky with Yacht gambling, the Zubmarine is the most expensive ship to acquire.

The best ship in terms of cost is the Tramp Steamer, followed by the Zee-clipper. (Though the Zee-clipper's price increase is not necessarily worth it for the benefit, unless you plan to zail a lot.)

Card Benefits

This sub-section is likely no longer accurate as of July 2015 due to a change in how cards work. Unique cards still seem to be applicable, though.

Ships also affect the cards you draw while zailing. While on the Unterzee, your deck is drawn from 12 to 14 cards:

7 cards can be drawn anywhere;

5 cards are linked to your current Troubled Waters;

(1 card appears when Embarking on a Voyage of Scientific Discovery;)

and the ships have 1 unique card each. Additionally, each ship unlocks an option on two other cards, except the Tramp Steamer.

Although many cards provide Appalling Secrets, the rewards in the Unterzee are poorer than those in Fallen London or Hunter's Keep, so you will usually want to cross the Unterzee as fast as possible.

This means that in terms of cards, the best ship is the Swift Zee-clipper, because its unique card is the best for granting speedy progress. But the difference is, again, marginal. The Zubmarine is barely better than the Yacht, but the Yacht also

The Tramp Steamer unlocks no cards and no options. This is actually where the Tramp Steamer shines. The Yacht's unique card is not good, and the Zubmarine's card is merely okay. (However, the Zee-clipper's card is great.)

Conversely, you will miss out on any benefits associated with the other ships.

The Swift Zee-clipper unlocks a unique card that is, well swift: it significantly accelerates your progress. Almost certainly the best unique card.

Its first card option unlock is at middling Troubled Waters and is pretty good (advancing progress), and a card option unlock at maximum Troubled Waters which lets you avoid a dangerous luck challenge. You'll rarely be at max Troubled Waters unless you've done it on purpose to get a Plated Seal, but it's a nice option if you need it.

The Zubmarine unlocks a unique card that reduces your Troubled Waters Menace along with progressing your journey, which is not quite as nice as the Zee-clipper (since Troubled Waters is not that dangerous), but better than the Yacht's unique card.

The Zubmarine has perhaps the best card option unlock, on the Killing Wind card, which appears at all stages of the journey. The Zubmarine option allows you to ignore the dangerous luck challenge and increase your progress (unlike the luck-avoidance options for the other ships).

It also has a mediocre card option unlock at middling Troubled Waters which does nothing for your progress or Troubled Waters.

The Majestic Pleasure Yacht unlocks a unique card worth 1.62 echoes and 1 CP Persuasive, which is decent. However, it does nothing for your progress or Troubled Waters. This is the least useful unique card.

The Yacht has the only card option unlock in Calm Waters (where you will spend most of your trip unless you have a specific reason not to) allowing you to invite passengers of another ship to a party. Unlike the Yacht's unique card, this option is very much worth it, because it gives you 5 x Secluded Addresses and 1 x Scarlet Stockings, worth 2.9 echoes! (Additionally, if you're kicked from Court and finished with the Big Rat, Secluded Addresses can be very difficult to come by.) It also increase Troubled Waters & Scandal (not usually serious), and does not progress your trip (more serious). Also gives Hedonist CP (up to 9 or 10).

Like the Clipper, the Yacht also has a card option unlock at maximum Troubled Waters which lets you completely ignore a dangerous luck challenge and decreases Troubled Waters. Again, you'll rarely be at max Troubled Waters unless you've done it on purpose to get a Plated Seal, but it's a nice option if you need it.

Summary

If you care about Notability the most, get the Majestic Pleasure Yacht.

If you intend to zail mostly calmly (as is normal) and care about profit, get the Majestic Pleasure Yacht.

If you want to split the difference between speed, Troubled Waters benefits, and Notability benefit, then get the Zubmarine.

If you care about your Bizarre score the most, get the Zubmarine.

If you care about speedily getting to your destination the most, get the Swift Zee-clipper.

If you don't care about Notability benefits, get the Swift Zee-clipper.

If you just don't want to worry about it (no real upsides or downsides), get the Tramp Steamer.

If you don't want to break the bank (or worry about grinding), get the Tramp Steamer.

If you like a ship's aesthetics the best, then get that ship. As explained above, the in-game differences are fairly marginal!

Zailing

Once you have your ship…

Much of the following section is doubly out of date as of July 2015.

You can set sail. It costs 100 Rostygold to set sail, but that is only one action at Watchmaker's Hill. The difficult Watchful challenge on setting sail can be happily failed - it just grants a small reward (IIRC worth ~1 Echo).

When you start your journey, you'll be healed one point of wounds.

Things to know: The Broad Unterzee has 3 states, depending on the weather: Calm Seas, Lashing Waves, or Fury of the Unterzee. The more recklessly you sail, the worse the weather. You will not have enough opportunity cards to cross the Unterzee unless you spend several real world hours on the trip. So when should you use them?
The Pleasure Yacht has a bonus card in Calm Seas, so spend early.
Both the Zub and Yacht have a bonus card in Lashing Waves, so spend later.

Cards can only be spent in their appropriate weather, so be careful to spend all Calm Seas cards before entering Lashing Waves (happens when Troubled Waters reaches 7). Actions and cards on average provide about equal amounts of progress and trouble, so you should reach your destination before entering the Fury unless you are very unfortunate.
The "A Mountain of the Unterzee" card is useful initially, as you have no progress for an unlucky result to reduce; however avoid it after that. "A Corvette of Her Majesty's Navy" is very useful if your suspicion > 5, dramatically increasing either your progress or troubled waters; but useless if your suspicion is < 5. Best to max out suspicion before heading to zee, as escaping from new Newgate removes all suspicion - your suspicion can easly reach 10 or more at zee, without making escape any more difficult.

Where to first?

Neither Mutton Island nor Hunter's Keep allow access to your hand. However any cards in hand are retained and become available when you return to zee. Landing resets your Troubled Waters Menace, so Calm Seas cards that were useless at the end of the trip will be usable on the return voyage.

Mutton Island:
When on Mutton Island: there is a rare success available for "The Mutton Island Wind"; it can also be used to increase Stormy eyed. Be sure to visit the Cock and Magpie (at least once, and up to 6 times) once time passing >6, and when you return to London revisit the Carnival. Finally, there is an action only available here that unlocks when Watchful reaches 140. Worth going to for the story, but the poor rewards mean that it is probably not worth revisiting.

Hunter's Keep: this is particularly tempting if you already have a Stone Tentacle Key from the Duchess! Hunter's Keep is the more profitable of the two locations, so come here for loot. Important tip towards the end of Time Passing: visit the Well *after* playing a Game of Charades (or at least wait until Time Passing =10), but *before* hearing the winning sister's concluding story.

Into the Fury of The Unterzee

Much of the following section is doubly out of date as of July 2015.

When monster hunting for the Bishop of Southwark, you'll be heading into the Fury… this is harder than it looks. "Steam Boldly/Make it up as you go" is a good opening move, as this rapidly increases both Troubled Waters & Approaching Journey's End: however this option locks when Troubled Waters hits 10. At this point you will need to juggle between opportunity cards and the Steam Prudently/A Cautious Captain option. Steam Prudently/A Cautious Captain locks at Troubled Waters 11.

All storylets lock when Approaching Journey's End reaches 9, forcing you to rely exclusively on opportunity cards: A Ship of Zealots, A Tiny Coral Island, A Shape in the Depths are all good choices; A Blanket of Fog is also acceptable. Failing The Clinging Coral Mass is the best of all. The other cards though will likely reduce either your Troubled Waters or Approaching Journey's End progress, making them counterproductive.

[The following section is out of date. Until July 2015, Plated Seals were obtained via a pinned storylet at under Steam Boldly at high Troubled Waters, and acquiring one sets Approaching Journey's End lower. After July 2015, they are obtained differently — see elsewhere for information.]

Once you have reached the Fury, cycle cards until you draw the Cold, Calm Waters card. Be wary of using other cards! Most 'good' cards will reduce your Troubled Waters. The Clinging Coral Mass, Those engines don't sound healthy/Hoist the black flag, The Killing Wind/Make Your Depth Fifteen Fathoms are useful if your Approaching Journey's End < 9 though.

Once you have your Plated Seal, you can head home - as Approaching Journey's End should be 9, this will likely be 1 action (so arguably you found the monster splashing in the Stolen River!) It does not appear possible to collect multiple Plated Seals.

[EDIT: This tip no longer works] If a Fury card reduces your Approaching Journey's End progress to 0, and you have a counterfeit head of John the Baptist, consider kissing it: this sends you to the Tomb Colonies, which may get you home faster and will allow you to collect a Tomb-Lion. [a counterfeit head now merely increases your Scandal].

This unlocks an additional card, "The Fleet of Truth", and a card option to "Share your Research with a Fellow Scholar". "The Fleet of Truth" is very useful, providing 2 change points of progress and 15 research notes! It is possible, at least in theory, to complete a journey just by using this one card repeatedly. "Share your Research with a Fellow Scholar" is a social card, and does not provide any progress - interesting, but not ideal. As you will likely be ejected from the new islands multiple times, there is no pressure to collect a Plated Seal on any specific journey; best to focus on crossing the Unterzee and head for the Fury when the luck of the draw pushes your Troubled Waters up.